Wave filter



Jul 13, 1937. R. B. BLACKMAN WAVE FILTER Filed April 20, 1935 3 Sheets-Sheet 2 13.13 .c Ev

E T R. $512 C? MAN A TTORNEV atented July 13, 1937 lli ll'l'ED STATES EQAATESET QEFMQE Eeil Telephone Laboratories, Incorporated,

New York, N. Y, a corporation of New York April 20, 1935, Serial No. l'iAEl 14 Claims.

lhis invention relates to wave filters and more particularly to wave filters using mechanical vibratory elements.

The principal object of the invention is to provide a mechanical vibratory structure which is capable of transmitting vibrations in a wide frequency range and at relatively high frequencies such as are used for carrier telephone transmission. Another object is to reduce the cost of band selective filters for high frequency transmission systems.

In the wave filters of the invention the mechanical vibratory system comprises a longitudinal stretched wire which acts as a main transmission 15 line and a plurality of stretched wires coupled transversely thereto which act as loading impedances. The end transverse wires are disposed in the air-gaps of electromagnets and are included in separate electric circuits whereby they can 30 function as driving means for converting electrical oscillations into mechanical vibrations or as receiving means for effecting the reverse transformation.

Particular features of the invention relate to the tuning of the wires whereby a continuous transmission band may be provided and to the proportioning of the mechanical impedances of the wires for the control of the width of the transmission band.

30 The nature of the invention will be more fully understood from the following detailed description and the attached drawings, of which Fig. 1 is a diagrammatic representation of one embodiment of the invention;

35 Fig. 2 shows schematically the arrangement of the electrical circuits and the mechanical vibratory system of the system of Fig. 1;

Figs. 3, 4, 5 and 6 illustrate the mechanical construction and details thereof of the system i of Fig. 1;

Figs. '7, 8, 9, 10 and 11 are schematic diagrams illustrative of the principles of the invention; and

Fig. 12 is a schematic representation of a modi- 5 fied form of the invention.

ill

Description of physical structure Referring to the drawings, a schematic arrangement of the magnetic and mechanical vi- .30 bratory systems of one embodiment of the invention is shown in l, in which, for the sake of clearness, much of the detail structure has been omitted. The magnetic system comprises a permanent magnet l! provided with three pole- 55 pieces l2, l2, and it which are arranged to pro- (Cl. 178--4l4) vide two separated air-gaps in the form of narrow slits parallel to each other. The vibratory system consists of a pair of stretched actuating wires l5 and 55' disposed in the respective air-gaps of the magnetic system, a stretched coupling wire 5 l5 lying perpendicular to the actuating wires and contacting therewith at their midpoints, and a set of loading wires ll, ll, and is disposed transversely of wire it and in contact therewith at their midpoints. Wires ll and H are arranged 10 to contact with the coupling wire H5 at the same points as wires l5 and i5 and are disposed diagonally to avoid interference with these Wires and also to remove them from the influence of the magnetic field. The supports for the 15 stretched wires are not shown in Fig. l, but are illustrated in Figs. 3, 4, 5, and 6, the details of which will be described later. Pole-pieces l2 and i2 may be secured by screws directly to the magnet. Pole-piece i3 is supported on a plate M of non-magnetic metal which in turn is rigidly secured to the magnet. The several pole-pieces are shaped to provide mechanical clearance for all of the wires of the vibratory system and are notched in the manner indicated in the drawings to accom- 5 modate diagonal Wires El and ll without subjecting them to the influence of the magnetic field.

Referring to Fig. 3, which shows the details of a practical construction partially disassembled for clarity, the coupling wire it and the transverse loading wires ll, H, and i8 are carried on a removable plate it which is arranged to be supported from the magnetic structure by brackets 2| and El and guide pins 22. An end view of the structure with the plate E9 in position is shown in Fig. 4. Vertical adjustment of the plate i9 is provided for by means of collared screws 23, one at each end, which engage the plate and are threaded into brackets 2i and El. By this means an ade- 4O quate mechanical contact between the driving wires the coupling wire it can be assured. The coupling wire it is supported from plate 59 by bracket members 24 and 25 the latter of which includes a tensioning arrangement consisting of a hinged lever arm 25 to which the end of the wire is attached and an adjusting screw and nut 27.

The loading wires are all similarly mounted on tensioning holders such as ti which are adjustably supported from plate 59. Details of these holders and of their supporting arrangements are shown in Fig. 5. At one end of the holder an anchor plate 32 is attached to which the stretched wire is secured. At the other end an adjustable tensioning lever is provided similar to that used for tensicning the coupling wire Hi. The details of the tensioning lever and the adjusting screw and nut are clearly shown. The

holder is carried on plate l9 by guide pins 28 and 28 which are rigidly attached to the plate and engage in close fitting holes in the holder. Vertical adjustment is provided by means of screw 29 which is threaded into the holder and passes through a clearance hole in plate 59. Spring 39 which encircles screw 2Q and abuts against the holder and the plate, serves to keep the holder in its adjusted position.

In the assembly of the coupling and loading wires it is preferable that diagonal wires if and H should bear on the top side of the coupling wire and transverse wire it on the under side.

The driving wires l5 and I5 are supported directly from the magnetic structure and are pro-- vided with adjustable tensicning means similar to those for the other wires. Details of the mounting are shown in Fig. 6, only the essential parts of the magnetic structure being indicated. The wire [5 is attached at one end to an anchor plate 33 mounted on plate l4 and at the other to a tensioning support comprising bridge piece 34 and tensioning lever 35. Anchor plate 33 and bridge piece 34 are insulated from plate l4 by plates 35 and 31 of insulating material and are attached to plate i i by suitably insulated screws. This is necessary since the wires l5 and i5 carry the input and output electrical currents. While the other wires of the system do not carry electrical currents it is preferable that they should be insulated in similar manner to the driving wires, at least at one end of each wire. The symmetry of the wire structure prevents the transmission of current from the one driving wire to the other through the coupling wire l6.

Theory of operation and design Before discussing the detailed theory of the invention the operation of the filter will be described briefly with reference to Fig. 2. In this figure, which is a schematic of the stretched wire system and its connections to the cooperating electrical circuits, the filter is shown connected between electrical input terminals T1 and T2 and output terminals T3 and T4 to which are connected resistive terminal impedances RT. In series with one of the terminal resistances is included a Wave source of voltage E.

Current from the source causes the driving wire I5 to vibrate transversely to the direction of the magnetic field in the air-gap in which the wire is situated. The vibrations of wire i5 are transmitted to wire 15 through coupling wire Hi. Vibrations or" wire iii in its magnetic field induce corresponding electromotive forces which cause currents to flow in the output circuit. The bandpass characteristic is obtained by proper dimensioning and tuning of the driving wires [5 and i5 and coupling wire I6 and by loading the latter at suitable points by the transverse wires IT, if, and I8, also properly dimensioned and tuned.

The manner in which the several wires must be tuned and proportioned to provide a single broadband transmission characteristic will be under stood from the following analysis.

It will be observed that the transducing means, namely stretched wires l5 and i5, whereby conversion of the energy from electrical to mechanical vibrations is effected, are flexible elements the different points of which partake of different motions. The reaction in the electrical system. due to the motion and the resulting mechanical force at the middle point where coupling to wire it is effected will therefore have somewhat com- Let l=length of the wire in centimeters,

linear density of the wire in grams per centimeter,

T tension in the wire in dynes,

li magnetic flux density in the air-gap in c. g. s. units, and

I=current in the wire in c. g. s. units.

An elemental portion of the wire of length dm at a distance a: from the mid-point will move under the action of two forces, one a force fiIdx due to the current and the other a mechanical force p equal to the difference of the transverse components of the tension 1 at the two ends of the element, that is, to the decrement -dp of the transverse mechanical force. These forces are opposed by the mass-acceleration reaction of the element, giving rise to the relationship where y denotes the transverse displacement. Assuming, the motion to be sinusoidal and of pulsatance w, Equation 1 may be rewritten as BIdx-dP pdx where denotes the transverse velocity.

Due to the tension 1' in the wire each elemental length has a transverse stillness equal to T/dx. The change in the lateral displacement from one end of the element to the other due to the transverse force p is therefore given by dx y -1 and the change of the transverse velocity by a; T df Assuming p to vary sinusoidally with pulsatance w, this equation becomes.

dj ,0: 5; J ;P

From Equations 2 and 3 is obtained T Y+J T 0 (4) which expresses the motion of the wire. In deriving Equations 3 and 4, it is assumed that the wire has a fiexural stiffness, due to its dimensions and material, which is negligibly small in com-- parison with the flexural stiffness due to the tension. I have found that this assumption is justified in practice and that the eifects of the fiexural stiffness of the wire itself are negligible except at frequencies well removed from the operating frequencies of the filters of the invention.

Equation 4 may be solved for each half of the wire to give the total mechanical reaction at the mid-point due to that half. Since each half will contribute the same reaction as the other half the reaction of the whole Wire is simply twice that of either half. Measuring a: from the midpoint of the wire the velocity y at the point at is given by where 1110 is the velocity at the mid-point and L 27Tfo in being the fundamental resonance frequency of the whole wire.

The mechanical reaction at the mid-point due to the half wire is obtained from Equation 5 by means of Equation 3. Denoting this reaction by 270, Equation 3 gives,

Performing the differentiation indicated and substituting for we, where it appears in the resulting coeflicients, the value given in Equation 6, the

' mid-point reaction is found to be 7H0 11 To Assuming that a driving force F is applied to the wire at its mid-point and that a mechanical load of impedance Z is attached at the driving point, the equation for the resultant motion of the midpoint is cot (10) On the electrical side the electromotive force, at the wire terminals, is given by which, when the integration is performed be comes where R is the electrical resistance of the wire. Equations 10 and 12 have the form F=Ay GI and E: Gym-BI where A and B represent mechanical and electrical impedances, respectively, and G is the force factor of the transducer. The force factor has Since the phase constant of the whole wire is equal to rah/p7; the angle 9 represents the phase constant of onequarter of the wire. The electrical impedance B has the value 2 R tan 9) Jwp 6 which, since may be written as sin 29 .Llsin 29 jw 4- p] 29 eep 29 The mechanical impedance A consists of three parts, first the load impedance Z, second, a component 1 /1; tan 6 which is the impedance of a short-circuited uniform line of characteristic impedance stant o with their remote terminals respectively short-circuited and open-circuited.

A more convenient equivalent system is shown schematically in Fig. 9. This: equivalent is arrived at from that of Fig. '7 by a transformation of the portion between the dotted lines mat and 11 The first step in the transformation is indicated by the schematic of Fig. 8. The force factor G is replaced by the equivalent combination of a new force factor G of value 6] sin 9 e (16) and an ideal transformer having a transformation ratio cos 9:1. The electrical impedance Z92 is replaced by an equivalent shunt impedance on the mechanical side of value ZPZ sin 29 The combination of the ideal transformer with this shunt impedance and the series impedance 7K tan 6 is equivalent to a section of uniform line of characteristic impedance K and phase angle e included in the circuit as indicated at 4B in Fig. 9.

The electrical impedance Z51 is of the character of a capacity, the value of which is proportional to the mass of the driving wire but variable with frequency in accordance with the inverse of the factor (1-sin 26/29). The magnitude of the impedance is small and may be neglected in most instances or, if desired, may be compensated by means of an inductance of appropriate value.

The line elements appearing in Fig. 9 have each a phase constant 9 and hence correspond in length to one-quarter of the driving wire.

The complete mechanical portion of the filter may be considered to include all the elements to the right of the vertical line ZZ' in Fig. 9, the load impedance Z being that due to the other wires of the system including wire I5 of the second transducer.

A schematic of the complete mechanical portion is shown in Fig. 10, the various elements being represented as transmission lines in accordance with electrical conventions. The system comprises a series of sections of uniform lines 49, 42, 44 and 46, connected in tandem, and intermediate series impedances 4!, 43 and 45, consisting of sections of uniform line open-circuited at their remote ends. The principal parameters of the line elements are proportioned as: follows. The reasons for these proportions and their relationships to the wire dimensions are discussed later. The tandem connected lines all have characteristic impedances of value K while the lines constituting the series impedances have characteristic impedances 2712K, m being a numerical factor greater than unity. The phase constants of the intermediate lines 42 and 44 are equal to 29 and those of all the other line sections are equal to 6.

With these proportions the whole filter consists of three tandem connected similar symmetrical sections, each of the type shown in Fig. 11 and consisting of two line sections of characteristic impedance K and phase constant 9, separated by a series impedance constituted by an open circuit line of characteristic impedance 2mK and phase angle 6.

The relationship of the various line sections of Fig. 10 to the several wires of the filter is as follows:

Line section is contributed by the electromechanical transducer system as already described. Line section 46 is a corresponding element introduced by the second transducer comprising driving wire l5. Line sections 42 and 44 represent the two intermediate sections of coupling wire I6, designated b and c in Fig. 2, through which the vibrations are transmitted from wire IE to wire l5. Since sections 40 and 46 have characteristic impedances K and phase constants 6, it follows sections 42 and. 44 must have the same characteristic impedance and phase constants 29 to provide the symmetrical character of the individual filter sections. The characteristic impedance of the transducer wires thus determines the characteristic impedance of the coupling wire.

Line sections 4!, 43 and correspond to the loading elements. Line section 4| represents a combination of the following components: first, the impedance 7'K cot 9 of element 39 contributed by transducer wire l5; second, the impedance of the end portion a of the coupling wire, which also acts as a loading impedance; and third, the joint impedance of the two halves of diagonal wire l1. All of these components correspond to uniform lines open-circuited at their outer ends.

The element 39 entering into the above combination from the transducer has a phase constant equal to 9. If each of the other elements be proportioned to have the same phase constant, the resultant impedance of the combination will be that of a single open-circuited line of phase constant 9 and characteristic impedance equal to the sum of the individual characteristic impedances.

Line element 43 represents the sum of the impedances of the two halves of transverse wire [8, each half being an open circuit line which, in accordance with the symmetry of the system, must have a phase constant 9. Line element 45 represents a combination similar to element 4| involving the two halves of wire l1, end section at of the coupling wire and the series impedance contributed by transducer wire I5. The contribution by the transducer wires of effective loading impedances of value 7'K cot 9 determines the phase constants of the other loading elements. Further, since the end sections of coupling wire l6 also constitute loading impedances, the phase constants of the several sections of the coupling wire are likewise determined by the transducer wire proportions.

The characteristic impedances of the diagonal wires I1 and I? must be such that with their associated elements they contribute a characteristic impedance 2mK corresponding to that of line section 43. This impedance is twice that of the wire [8 since each half of the wire contributes equally to the load. Since the transducer wires and the end sections of the coupling wire each contribute a characteristic impedance K it follows that wires I! and I1 must have characteristic impedances equal to (ml)K.

The function of the loading wires in controlling the width of the transmission band of the filter may be seen from an examination of the image impedance, which is the same as that of the filter section of Fig. 11. The image impedance of the section can be computed by standard formulae from the open-circuit and short-circuit impedances, its value being given by where W denotes the image impedance.

Equation 1'7 shows that the impedance has a tan 0:425 (18) The filter has an indefinite number of transmission bands all of uniform width and centered about the frequencies for which cot e is zero or 6 is an odd multiple of vr/Z. From Equation 14 giving the value of 9 it follows that the midfrequencies of the successive bands are 2ft), 6%, 1010, and so on. The lowest frequency band is the only one of interest, the mid-band frequency in this case being twice the fundamental resonance frequency of the driving wires.

Equations 17 and 18 indicate that the width of the band is dependent on the value of m and decreases as m increases. tained when m is equal to unity, the band limits in this case being in and 31%). Since the characteristic impedances of diagonal wires I! and H are equal to (m-l) K, it follows that in the limiting case these wires would have zero character- The widest band is obistic impedance, that is, the diagonal wires would be absent. By the use of the diagonal wires and a correspondingly proportioned central loading wire, the band width is made subject to control. While the mechanical portion of the system has an indefinite number of bands only the lowest frequency band appears in the over-all electromechanical system. The elimination of the higher frequency bands is due to the frequency characteristic of the electro-mechanical transducer. Referring to Fig. 9, it will be seen that the mechanical portion is coupled to the electrical circuits by force factors G, the value of which is given by Equation 15 and is variable with frequency. At the mid-frequency of the first band the phase constant 9 has the value 1r/2, the force factor having the value G1 given by G1I=B I 'II' and at the mid-frequencies of the successively higher bands being respectively A, A etc. as great. Since the efficiency of transmission is proportional to the square of the force factor, the loss in the higher frequency bands is very large.

The impedance Zel, which is added to the electrical circuit by the transducer has the value, given by Equation 15,

1 B 1 4 sin 26 O Z01 ja 4 p1 e which at the mid-frequency of the lowest transmission band becomes Fig. 2 shows inductances L inserted in the input and output electrical circuits in series with the driving wires.

In the construction of the filter it is preferable to use aluminum alloy such as duralumin for the driving wires l5 and I5. Such materials have high tensile strength and, in addition to having low density, have. relatively high electrical conductivity. Because of the low density, the length of the wire for a given resonance frequency and tension will be greater than for other materials and hence will permit greater values of the force factor. The other wires may be of the same material, but in many cases steel piano wire may be preferred because of its greater tensile strength. In the case of the loading wires, the greater density of steel permits the relatively high characteristic impedances to be obtained without resorting to excessively large mechanical tensions.

If all of the wires are made of the same material and subject to the same mechanical tension, wires l1, 1'! and I8 will be of the same length, wires l5 and I5 twice as long and wire [6 three times as long. Their fundamental resonance frequencies will be inversely proportional to their lengths. Loading wires l1, l1 and I8 will resonate to the mid-frequency of the first transmission band or twice the resonance frequency f0 of the driving wires. Coupling wire It will resonate at a frequency two-thirds of the driving wire frequency.

When different materials are used for the several wires the required relationships of the phase constants and characteristic impedances can be maintained by appropriate adjustments of the lengths and diameters of the wires and of the mechanical tensions. The relationships of the fundamental resonance frequencies will remain unchanged. The lengths and diameters of the wires should be so chosen that the required resonances are obtained with mechanical tensions suitable for the material used.

The modified form of filter shown schematically in Fig. 12 differs from that of Figs. 1 and 2 in that the central loading wire [8 is omitted and the coupling wire is shortened by the length of one of the intermediate sections b or c. This modification is a two-section filter and represents the minimum number of sections that can be constructed. Obviously, as many additional sections as desired can be added by increasing the length of the coupling Wire and adding transverse wires corresponding to wire l8.

What is claimed is:

l. A wave filter comprising a longitudinal stretched wire and a plurality of transverse stretched wires coupled mechanically to said longitudinal wire at their mid-points and spaced apart along the length thereof, said wires being tuned with respect to each other and to a preassigned frequency whereby the system is responsive to vibrations in a frequency band centered about said preassigned frequency.

2. An electromechanical wave filter comprising a longitudinal stretched wire, a plurality of transverse stretched Wires coupled mechanically thereto at points spaced apart along the length thereof, magnetic means providing magnetic fields perpendicular to two of said transverse wires and separate electric circuits connected to the ends of said two transverse wires, said wires being tuned with respect to each other and to a preassigned frequency whereby the system has a transmission band in a frequency range centered about said preassigned frequencies.

3. An electromechanical wave filter comprising a longitudinal stretched wire, a plurality of transverse stretched wires coupled mechanically thereto at points spaced apart along the length there of, magnetic means providing magnetic fields perpendicular to the first and the last of said transverse wires, means for passing oscillatory electric currents through said first transverse wire whereby mechanical vibrations are produced, and means for deriving electric currents from said last transverse wire, said wires being tuned with respect to each other and to a preassigned frequency whereby the system has a transmission band in a frequency range centered about said preassigned frequencies.

4. An electromagnetic wave filter comprising a first electric circuit, a stretched wire included in series therein and disposed in a transverse magnetic field, a second electric circuit, a second stretched wire included in series in said second circuit and disposed in a transverse magnetic field, and mechanical coupling means between said stretched wires comprising a third stretched Wire coupled to said first and second wires at the mid-points thereof, said first and second wires being tuned alike to a preassigned frequency and the portion of said coupling wire between said first and second wires being tuned to a sub-harmonic of said preassigned frequency.

5. An electromechanical wave filter comprising a longitudinal stretched wire, a plurality of transverse stretched wires engaging said longitudinal wire at their mid-points and spaced apart on said longitudinal wire so that their separation from each other is twice the distance from each end of the longitudinal wire to the nearest transverse wire, magnet systems providing magnetic fields perpendicular to two, of said transverse wires and separate electric circuits connected to the ends of each of said two transverse wires.

6. A broad band wave filter comprising a longitudinal stretched wire, and a plurality of transverse stretched wires engaging said longitudinal wire at their mid-points and spacedat equal intervals therealong, the first and the last of said transverse wires being tuned alike to a preassigned frequency and said longitudinal wire being tuned to a lower frequency such that the fractional portions thereof between said transverse wires are resonant at twice said preassigned frequency.

'7. A broad band wave filter comprising a longitudinal stretched wire and a plurality of transverse stretched wires engaging said longitudinal wire at their mid points and spaced uniformly apart on said longitudinal wire at the mid-points of equal sections thereof, the first and the last said transverse wires being tuned alike to a preassigned frequency and said longitudinal wire being tuned to a lower frequency equal to twice said preassigned frequency divided by the number of the coupling points to the transverse wires.

8. An electromechanical wave filter comprising a longitudinal stretched wire, a pair of transducer wires stretched transversely across said longitudinal wire at equal distances I from the opposite ends thereof and coupled thereto at their mid-points, additional transverse wires coupled to said longitudinal wire at their midpoints and spaced apart uniformly by distances 21, magnetic means providing magnetic fields transverse to said transducer wires, and separate electric circuits including said receiver wires, two of said additional transverse wires being coupled to said longitudinal wire at the same points as the said receiver wires and being disposed outside the fields of said magnetic means.

9. An electromechanical filter in accordance with claim 8 in which the transducer wires are tuned alike to a preassigned frequency and the additional transverse wires are tuned alike to a frequency twice as great.

10. An electromechanical wave filter in accordance with claim 8 in which the transducer wires are tuned alike to the mid-frequency of a preassigned transmission band and the additional transverse wires and the intermediate sections of the longitudinal wire are tuned alike to a frequency twice as great.

11. An electromechanical wave filter in accordance with claim 8 in which the transducer wires and the longitudinal wire have equal characteristic impedances of value K and in which the additional transverse wires are proportioned to provide loads of characteristic impedance ZmK, 172 being a numerical factor greater than unity.

12. A broad band wave filter comprising a longitudinal stretched wire and a plurality of substantially coplanar transverse stretched wires coupled mechanically to said longitudinal wire at points spaced apart along the length thereof, said longitudinal and said transverse wires being so tuned that each of the free lengths thereof has a natural frequency of transverse vibration at a frequency integrally related to a preassigned frequency, whereby the system transmits freely vibrations in a frequency band centered about said preassigned frequency.

13. A broad band wave filter comprising a longitudinal stretched wire, a plurality of substantially coplanar transverse stretched wires coupled mechanically to said longitudinal wire at points spaced apart along the length thereof, means for applying transverse vibratory forces to one of said transverse wires, and means responsive to vibratory motion coupled to another of said transverse wires, said wires being so tuned that each of the free lengths thereof has a natural frequency of transverse vibration at a frequency integrally related to a preassigned frequency, whereby the system transmits freely vibrations in a frequency band centered about said preassigned frequency.

14. A wave filter comprising a longitudinal stretched wire, a plurality of substantially coplanar transverse stretched wires coupled mechanically at their mid-points to said longitudinal wire at the centers of equal sections thereof, means for applying transverse vibratory forces to one of said transverse wires adjacent one end of said longitudinal wire, and means responsive to vibratory motion coupled to another of said transverse wires, said wires being tuned to frequencies integrally related to a preassigned frequency whereby the system is adapted to transmit selectively vibrations in a frequency band centered about said preassigned frequency.

RALPH B. BLACKMAN. 

